we obtain a "central planner" problem (or cooperative game) which has been showed to converge to a stochastic control problem of McKean-Vlasov type, see [1]}, [2]}, [3]}.
The analysis of the LDP in this case follows the same steps as in the non-cooperative game described above.
To avoid repeating the proof, in the case of cooperative games we focus on a linear quadratic game and again derive an LDP, see Section  for details.
